Case Theories: Agree vs. Dependent Case vs. Voice-Based

@cite{baker-2015} @cite{chomsky-2000} @cite{chomsky-2001} @cite{marantz-1991} @cite{ozaki-2026} @cite{scott-2023} @cite{woolford-1997} @cite{woolford-2006}

Three competing theories of abstract case assignment in Minimalism:

1. Agree-based case: Case is a feature valued via the Agree operation. T values NOM on its specifier; v* values ACC on its complement. Case requires a specific functional head as assigner. The Case Filter (CaseFilter.lean) enforces that all DPs receive Case.

2. Dependent case: Case is determined by the configuration of NPs in a Spell-Out domain. An NP c-commanded by another caseless NP gets ACC (in accusative languages); unmarked NPs get NOM. No specific head is needed.

3. Voice-based case (@cite{scott-2023}, building on @cite{woolford-1997}): @cite{woolford-1997} argues that ERG is a lexical/inherent Case (like dative), assigned at D-structure in conjunction with θ-role assignment. @cite{scott-2023} reframes this in a modern Voice-based architecture: ERG is inherent case from Voice (tied to the agent θ-role), ACC is structural from Voice (object licensing), ABS is structural from Infl. Case is directly determined by argument structure, not by configuration or feature checking. This gives a tripartite underlying system (ERG ≠ ACC ≠ ABS) visible through agreement patterns.

Key Divergences

Unaccusatives with ACC (Agree vs. Dependent):

• Agree predicts a gap: no v* → no ACC assigner
• Dependent case: two caseless NPs suffice regardless of Voice

Tripartite alignment (all three):

• Agree: requires two distinct probes (T for NOM, v* for ACC)
• Dependent case: dependent ACC on lower NP, unmarked NOM
• Voice-based: ERG (inherent from Voice), ACC (structural from Voice), ABS (structural from Infl) — three heads, three cases

Voice's role:

• Agree: v* is a phase head that can probe for ACC
• Dependent case: Voice is irrelevant to the algorithm
• Voice-based: Voice directly assigns ERG/ACC based on θ-role

theorem Phenomena.Case.Compare.agree_predicts_no_acc_for_unaccusatives : Minimalism.voiceAnticausative.phaseHead = false

Under Agree, ACC requires a phase head (v*). Anticausative Voice is not a phase head, so Agree predicts no ACC for unaccusatives.

theorem Phenomena.Case.Compare.dependent_case_acc_voice_independent : have nps := [{ label := "higher", lexicalCase := none }, { label := "lower", lexicalCase := none }]; Minimalism.getCaseOf "lower" (Minimalism.assignCases Minimalism.CaseLanguageType.accusative nps) = some Minimalism.CaseVal.acc

Under dependent case, ACC only requires two caseless NPs. Voice flavor plays no role in the algorithm.

theorem Phenomena.Case.Compare.single_np_gets_nom : have nps := [{ label := "sole", lexicalCase := none }]; Minimalism.getCaseOf "sole" (Minimalism.assignCases Minimalism.CaseLanguageType.accusative nps) = some Minimalism.CaseVal.nom

Both theories correctly assign NOM to the sole argument of a simple unaccusative (one NP, no case competitor).

theorem Phenomena.Case.Compare.transitive_acc : have nps := [{ label := "subject", lexicalCase := none }, { label := "object", lexicalCase := none }]; Minimalism.getCaseOf "object" (Minimalism.assignCases Minimalism.CaseLanguageType.accusative nps) = some Minimalism.CaseVal.acc ∧ Minimalism.getCaseOf "subject" (Minimalism.assignCases Minimalism.CaseLanguageType.accusative nps) = some Minimalism.CaseVal.nom

Both theories assign ACC in a standard transitive configuration (though they disagree on why: Agree says v* probes; dependent case says the lower NP gets ACC from configuration).

@cite{scott-2023} argues for Mam that case is assigned by three different heads: Voice assigns ERG (inherent, to agent) and ACC (structural, to patient), while Infl assigns ABS (structural, to intransitive S). This is neither Agree-based (no probe on T for NOM) nor dependent (ERG is inherent, not configurational).

theorem Phenomena.Case.Compare.voice_based_tripartite : Fragments.Mayan.Mam.MamArgPosition.agent.case ≠ Fragments.Mayan.Mam.MamArgPosition.patient.case ∧ Fragments.Mayan.Mam.MamArgPosition.agent.case ≠ Fragments.Mayan.Mam.MamArgPosition.intranS.case ∧ Fragments.Mayan.Mam.MamArgPosition.patient.case ≠ Fragments.Mayan.Mam.MamArgPosition.intranS.case

Voice-based case produces three distinct underlying cases. This is the tripartite system visible through agreement patterns.

theorem Phenomena.Case.Compare.dependent_case_tripartite : have nps := [{ label := "higher", lexicalCase := none }, { label := "lower", lexicalCase := none }]; Minimalism.getCaseOf "higher" (Minimalism.assignCases Minimalism.CaseLanguageType.tripartite nps) = some Minimalism.CaseVal.erg ∧ Minimalism.getCaseOf "lower" (Minimalism.assignCases Minimalism.CaseLanguageType.tripartite nps) = some Minimalism.CaseVal.acc

Dependent case also produces a tripartite system (ERG + ACC + ABS).

theorem Phenomena.Case.Compare.agree_voice_is_phase_head : Minimalism.voiceAgent.phaseHead = true

Agree-based: v* (agentive Voice) is a phase head, so can assign ACC.

theorem Phenomena.Case.Compare.agree_anticausative_no_acc : Minimalism.voiceAnticausative.phaseHead = false

Agree-based: anticausative Voice is NOT a phase head, so no ACC.

theorem Phenomena.Case.Compare.voice_assigns_case_by_position : Fragments.Mayan.Mam.MamArgPosition.agent.case = Core.Case.erg ∧ Fragments.Mayan.Mam.MamArgPosition.patient.case = Core.Case.acc ∧ Fragments.Mayan.Mam.MamArgPosition.intranS.case = Core.Case.abs

Voice-based: Voice assigns case DIRECTLY based on argument position, not via probing. The agent gets ERG, the patient gets ACC.

theorem Phenomena.Case.Compare.dependent_case_ignores_voice : have transitive := [{ label := "agent", lexicalCase := none }, { label := "theme", lexicalCase := none }]; have unaccusative := [{ label := "experiencer", lexicalCase := none }, { label := "theme", lexicalCase := none }]; Minimalism.getCaseOf "theme" (Minimalism.assignCases Minimalism.CaseLanguageType.accusative transitive) = Minimalism.getCaseOf "theme" (Minimalism.assignCases Minimalism.CaseLanguageType.accusative unaccusative)

Dependent case: Voice flavor is irrelevant. The algorithm only cares about NP configuration (higher vs. lower) and lexical case.

theorem Phenomena.Case.Compare.case_filter_example : Minimalism.satisfiesCaseFilter (Minimalism.DPFeatures.withCase [Minimalism.PhiFeature.person Core.Prominence.PersonLevel.first, Minimalism.PhiFeature.number Number.sg] Minimalism.CaseVal.nom) = true ∧ Minimalism.satisfiesCaseFilter (Minimalism.DPFeatures.withUnvaluedCase [Minimalism.PhiFeature.person Core.Prominence.PersonLevel.first, Minimalism.PhiFeature.number Number.sg]) = false

The Case Filter is the Agree-based enforcement: every DP must have valued Case at the interfaces. This presupposes Agree-based case assignment (DPs start with [uCase]).

Under dependent case, there is no [uCase] feature — case is assigned configurationally, so the Case Filter is unnecessary.

Under Voice-based case, the filter is implicit: case is inherent (from Voice for ERG/ACC) or structural (from Infl for ABS), and every argument position receives case by construction.

theorem Phenomena.Case.Compare.dependent_case_always_assigns : have nps := [{ label := "subj", lexicalCase := none }, { label := "obj", lexicalCase := none }]; ((Minimalism.assignCases Minimalism.CaseLanguageType.accusative nps).all fun (np : Minimalism.CasedNP) => np.case != Minimalism.CaseVal.obl) = true

Under dependent case, every NP in a domain receives case — the algorithm always assigns (lexical, dependent, or unmarked).